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QUANTIZING SL(N) SOLITONS AND THE HECKE ALGEBRA / Timothy Hollowood

International Journal of Modern Physics A, Volume: "A8", Issue: 05, Pages: 947 - 982

Swansea University Author: Timothy Hollowood

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Abstract

The problem of quantizing a class of two-dimensional integrable quantum field theories is considered. The classical equations of the theory are the complex $sl(n)$ affine Toda equations which admit soliton solutions with real masses. The classical scattering theory of the solitons is developed using...

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Published in: International Journal of Modern Physics A
ISSN: 0217-751X 1793-656X
Published: 1992
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URI: https://cronfa.swan.ac.uk/Record/cronfa28594
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spelling 2016-06-03T14:37:07.7223941 v2 28594 2016-06-03 QUANTIZING SL(N) SOLITONS AND THE HECKE ALGEBRA ea9ca59fc948276ff2ab547e91bdf0c2 0000-0002-3258-320X Timothy Hollowood Timothy Hollowood true false 2016-06-03 SPH The problem of quantizing a class of two-dimensional integrable quantum field theories is considered. The classical equations of the theory are the complex $sl(n)$ affine Toda equations which admit soliton solutions with real masses. The classical scattering theory of the solitons is developed using Hirota's solution techniques. A form for the soliton $S$-matrix is proposed based on the constraints of $S$-matrix theory, integrability and the requirement that the semi-classical limit is consistent with the semi-classical WKB quantization of the classical scattering theory. The proposed $S$-matrix is an intertwiner of the quantum group associated to $sl(n)$, where the deformation parameter is a function of the coupling constant. It is further shown that the $S$-matrix describes a non-unitary theory, which reflects the fact that the classical Hamiltonian is complex. The spectrum of the theory is found to consist of the basic solitons, scalar states (or breathers) and excited (or `breathing') solitons. It is also noted that the construction of the $S$-matrix is valid for any representation of the Hecke algebra, allowing the definition of restricted $S$-matrices, in which case the theory is Journal Article International Journal of Modern Physics A "A8" 05 947 982 0217-751X 1793-656X 31 3 1992 1992-03-31 10.1142/S0217751X93000370 http://inspirehep.net/record/333204 COLLEGE NANME Physics COLLEGE CODE SPH Swansea University 2016-06-03T14:37:07.7223941 2016-06-03T14:37:07.5351929 College of Science Physics Timothy Hollowood 0000-0002-3258-320X 1
title QUANTIZING SL(N) SOLITONS AND THE HECKE ALGEBRA
spellingShingle QUANTIZING SL(N) SOLITONS AND THE HECKE ALGEBRA
Timothy, Hollowood
title_short QUANTIZING SL(N) SOLITONS AND THE HECKE ALGEBRA
title_full QUANTIZING SL(N) SOLITONS AND THE HECKE ALGEBRA
title_fullStr QUANTIZING SL(N) SOLITONS AND THE HECKE ALGEBRA
title_full_unstemmed QUANTIZING SL(N) SOLITONS AND THE HECKE ALGEBRA
title_sort QUANTIZING SL(N) SOLITONS AND THE HECKE ALGEBRA
author_id_str_mv ea9ca59fc948276ff2ab547e91bdf0c2
author_id_fullname_str_mv ea9ca59fc948276ff2ab547e91bdf0c2_***_Timothy, Hollowood
author Timothy, Hollowood
author2 Timothy Hollowood
format Journal article
container_title International Journal of Modern Physics A
container_volume "A8"
container_issue 05
container_start_page 947
publishDate 1992
institution Swansea University
issn 0217-751X
1793-656X
doi_str_mv 10.1142/S0217751X93000370
college_str College of Science
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hierarchy_parent_title College of Science
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url http://inspirehep.net/record/333204
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description The problem of quantizing a class of two-dimensional integrable quantum field theories is considered. The classical equations of the theory are the complex $sl(n)$ affine Toda equations which admit soliton solutions with real masses. The classical scattering theory of the solitons is developed using Hirota's solution techniques. A form for the soliton $S$-matrix is proposed based on the constraints of $S$-matrix theory, integrability and the requirement that the semi-classical limit is consistent with the semi-classical WKB quantization of the classical scattering theory. The proposed $S$-matrix is an intertwiner of the quantum group associated to $sl(n)$, where the deformation parameter is a function of the coupling constant. It is further shown that the $S$-matrix describes a non-unitary theory, which reflects the fact that the classical Hamiltonian is complex. The spectrum of the theory is found to consist of the basic solitons, scalar states (or breathers) and excited (or `breathing') solitons. It is also noted that the construction of the $S$-matrix is valid for any representation of the Hecke algebra, allowing the definition of restricted $S$-matrices, in which case the theory is
published_date 1992-03-31T03:43:57Z
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